Question

What percent of $$44.8 \text { is } 8.27 ?$$

Short answer

8.27 is approximately 18.46% of 44.8.

Step-by-step solution

Identify the Values

Identify the whole value and the part value in the question. In this case, the whole value is 44.8 and the part value is 8.27.

Write the Percent Formula

Write the formula to find the percent: \( \text{Percent} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \).

Plug in the Known Values

Substitute the part and whole values into the formula: \( \text{Percent} = \left( \frac{8.27}{44.8} \right) \times 100 \).

Calculate the Division

First, divide the part by the whole: \( \frac{8.27}{44.8} \approx 0.18459821429 \).

Multiply by 100 to Find Percentage

Now multiply by 100 to find the percentage: \( 0.18459821429 \times 100 \approx 18.459821429 \).

Round the Result if Necessary

If rounding is required, round the result to the desired precision. For example, round to two decimal places: 18.46%.

Key concepts

Percent Formula

Understanding percentages is integral to various real-life applications, from calculating taxes to determining markdowns during sales. The percent formula is the foundation for these calculations. Simply put, it allows us to figure out what one quantity is as a percentage of another. The general formula is expressed as:
\[ \text{Percent} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \]
In this formula, 'Part' represents the portion of interest, while 'Whole' refers to the total or entire quantity. After dividing the 'Part' by the 'Whole', multiplying by 100 converts the decimal into a percentage, enabling easy interpretation of the result. This formula is versatile and can be applied in endless scenarios, making it a fundamental concept in mathematics.

Mathematical Problem Solving

Problem solving in mathematics requires a systematic approach to dissect and understand the problem before moving towards the solution. It often involves several steps that guide us to the final answer. Taking our exercise as an instance,

• Step 1: We identify the values we're working with—the 'Part' (8.27) and the 'Whole' (44.8).
• Step 2: We set up the percent formula.
• Step 3: We substitute known values into our formula.
• Step 4 and beyond: We perform the arithmetic operations to solve.

Breaking down problems into manageable steps can transform an overwhelming task into a series of straightforward calculations.

Division in Percentages

Division plays a pivotal role when it comes to calculating percentages. It allows us to determine what fraction the 'Part' is of the 'Whole'. This step is crucial before we multiply the result by 100 to convert it into a percentage. When performing division in percentages, accuracy is key, as it lays the groundwork for the entire calculation. For example:
\[ \frac{8.27}{44.8} \approx 0.1846 \]
Once we have this fraction, it becomes clear how large the 'Part' is relative to the 'Whole'. Careful division ensures that the subsequent steps yield an accurate percentage.

Arithmetic Operations

Arithmetic operations, including addition, subtraction, multiplication, and division, are the building blocks of most mathematical calculations. In the context of percentage calculations, multiplication and division are particularly essential. After dividing to find the ratio of the 'Part' to the 'Whole', we multiply by 100 to get the percentage. It's essentially a two-step process made of basic arithmetic operations:

• Division to determine the ratio or fraction: \[ \frac{\text{Part}}{\text{Whole}} \]
• Multiplication to convert this fraction into a percentage: \[ \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100 \]

Each operation must be performed correctly to ensure the final percentage reflects the true relationship between the 'Part' and the 'Whole'.